Zugzwang

One of the features of Christmas is the change it offers from our more usual routine. Whether it is family members seen only once a year, or the party games and feasting, or for some an annual trip to the local church, Christmas is for most people a complete break from the norms and worries of everyday life.

MPs too look forward to the Christmas break, for exactly the same reasons. And this year they will have welcomed even more than usual the opportunity to escape from the hothouse atmosphere of Westminster and the endless debate over Brexit, in which there is no clear way forward and no good outcomes. Many MPs are as fed up with the matter as much of the general public is; it has overwhelmed normal politics and most MPs have a large number of other issues building up in their in-tray that they would much rather be spending their time on. The army of BOBs – those “Bored of Brexit” – includes a fair number of the House of Commons in its ranks.

But just as the rest of us return to work in January to find that although it is a new year, the same old problems still confront us, so it is for MPs. Brexit has not gone away, and – unless Mrs May astounds everyone by once again putting off a vote on her deal – they will soon be called upon to decide on the matter.

And the choice in front of them is genuinely not easy. British politics is stuck with two most unusual problems, in that firstly the choice before MPs is a three-way choice (ie, May’s deal, no deal, 2nd referendum) not the more usual binary one (ie, to do something or not) and secondly the usual party discipline has collapsed – neither party has an agreed policy on the matter, with supporters of all three options in both major parties, and neither party leader has sufficient charisma, authority or support from their MPs to be able to impose their will or even some semblance of party discipline.

The lack of party discipline means that MPs are in the unusual position of being able to think for themselves (indeed one might cynically say that for once they are being forced to). Many will be aware of how their constituents feel and voted on the referendum, and whether out of a sense of democracy or simply in an attempt to preserve their seat at the next election, not a few will treat that as more important than what their party leadership thinks. The result is that the Whips offices, on both sides of the House, are unusually weak – they are less in control of their party’s vote than at almost any time in the last 15 years, since the early days of the Iraq and Afghanistan conflicts in fact, when the House was full of principled positions opposed to the party leaderships.

And the result of the three-way choice is that it is not just what MPs want most that they must factor in to how they vote but also what they fear most. Indeed, for many MPs it is not that one option of the three is much better than the other two, but that one is much worse, and must at all costs be avoided.

It is fairly clear that for Mrs May and her most loyal lieutenants, a second referendum is the outcome that they are keenest to avoid. Quite apart from the rejection of all of their efforts that this would signify, they have a genuine concern that it would be seen as breaking faith with the electorate, further undermining respect for the political process and creating a volatile and perhaps even dangerous mood in society at large. Nor, with the example of France’s gilets jaunes just across the Channel, are these fears of social unrest necessarily exaggerated – copycat politics is not new and civil disturbance cannot be ruled out.

For many MPs (and not just those who would prefer to remain in the EU), a no deal exit is the outcome that must be avoided, because of the potential damage they fear that it could do to the economy. And for the most ardent Brexiteers, it is Mrs May’s deal that they really fear, because it raises the possibility that the UK might never escape from the EU’s oversight and regulations. This is the BRINO outcome – “Brexit in name only” – and for the true Brexiteers it is more feared than a second referendum, which many in their ranks are confident they would win.

This sort of situation is known as a Condorcet paradox. The Marquis of Condorcet was an 18th century French philosopher and political theorist, and he demonstrated that in any three-way decision, the resulting choice is neither guaranteed to reflect the wishes of those voting nor independent of the voting method. The outcome is very likely to be against the wishes of more than half the voters, and in a three way choice where the majority of voters prefers outcome A to outcome B, outcome B to outcome C and outcome C to outcome A, the process is indeterminate and a re-run of the vote might see a totally different result[1].

What adds to the sense of uncertainty is that all three camps in the House are caught in a sort of Zugzwang[2] – they are safe if they do nothing, but if they force a vote they may end up triggering exactly the outcome they fear most. This is why May keeps postponing the vote on her deal, why the Brexiteers repeatedly pull their punches, why Corbyn vacillates between threats and inaction and why those favouring a second referendum (quite possibly the biggest of the various groupings in the House) nevertheless do not dare move first.

So, what will happen? On the surface the most likely outcome is now probably that the UK will leave the EU with no deal, if only because that is what will happen if nothing else happens first. And that undoubtedly gives the hard Brexiteers the initial advantage, though the mere fact that it is the most likely outcome makes it also the one many MPs will be striving the hardest to avoid at all costs.

It is precisely this sort of feedback loop from the balance of the situation to the voting intentions of MPs that forms the heart of the Condorcet paradox. Strictly speaking, because a default or “do-nothing” outcome does exist, the position is not a true Condorcet position. But Condorcet’s analysis is still useful in its examination of the dynamics of the three two-way decisions that can be constructed as sub-decisions of a three-way decision – which, given that MPs can only vote for or against any given motion, is the likely way the situation will be resolved. And the general conclusion of his work is that the order in which any multiple voting is carried out is critical, and therefore that those who control the process are well placed to engineer the outcome they most want.

So Mrs May may appear to have the initiative, in that she and her business managers control the business of the House and can decide what MPs vote on, when and in what order. But the Zugzwang nature of the situation remains. As long as she postpones a vote she stays in control. But whenever she makes a move, whatever that move is, she risks weakening her position. And she cannot do nothing for ever.

[1] The Liberal Democrat party is very familiar with Condorcet’s paradox, as they face it in almost every seat they contest. Perceptions on whether they have a chance of winning the seat, and tactics from supporters of their opponents, tend to matter much more than the party’s actual policies or the qualities of their candidate. This makes it a very frustrating party to run and an almost impossible one to campaign for.

[2] A term from chess. A player is said to be in Zugzwang if he or she is currently safe, but any move he make worsens his position. Because players are forced to move alternately, a player in Zugzwang has no option but to cause his own position harm.